It results change only in it's kinetic energy, it's KE will increase in accord with the work-energy theorem
No they say "Watch out it's the fuzz"
If its accelerating it will increase velocity in the direction of the acceleration which is perpendicular to the velocity.
Making a wire thicker has the same effect as making a road wider. It makes it easier for the electron traffic to flow. The resistance decreases, and the current (traffic) increases.